Problem 2 25 pts a block of mass m 54 kg at rest on a

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Problem 2 (25 pts.):A block of massM= 5.4 kg, at rest on a horizontal frictionless table, isattached to a rigid support by a spring of constantk= 6000 N/m which is initially uncompressed.A bullet of massm= 9.5 g and velocityvof magnitude 630 m/s strikes and becomes embeddedin the block. This compresses the spring and sets block and spring in simple harmonic motion.Determine:a) (8 pts.) the speed of the block immediately after the collision.b) (9 pts.) the amplitude of the harmonic motion.2c) (8 pts.) the frequency of the harmonic motion.M
Problem 3(25 pts.)The figure to the right shows a block Swith massM. The block is free to move along a horizontalfrictionless surface and connected, by a massless cord thatwraps over a frictionless pulley with massmand radius(I=mr2/2) to a second block H also of massm.The hangingblock H falls as the sliding block S accelerates to the right.a)(6 pts.)Draw force diagrams for blocks S and H and thepulley.s=Ma=mMM+32mgmaα=-a/rrb)(10 pts.)Find the linear acceleration of the rope.)c)(9 pts.)Find the magnitude of tension in the rope pulling on block S.Ts=Ma=mMM+32mgmaα=-a/r
Problem 4 (26 pts)As shown in the figure, anoverheadview of a thin uniform rod of length0.80 m and massM= 1.0 kg rotating horizontally at angular speed 20 rad/s about an axisthrough its center. A particle of massM/3 initially attached to one end is ejected from the rod bya small explosion and travels along a straight path that is perpendicular to the rod at the instant ofejection. The particle's final speedvp(after the ejection) is 11.0 m/s.a)(6 pts.) What is the angular momentum (magnitude anddirection) of the particle about the center of rod at themoment before the ejection?)